Explanation

(a)
$Since,\ slope\ of\ PQ = \frac{4 - 3}{1 - k} = \frac{1}{1 - k}$
$\therefore\$Slope of $AM = (k - 1)$
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$\therefore$ Equation of $AM$ is
$y - \frac{7}{2} = (k - 1)\left\lbrack x - \left( \frac{k + 1}{2} \right) \right\rbrack$
For $y$-intercept, $x = 0,$ $y = - 4$
$- 4 - \frac{7}{2} = - (k - 1)\left( \frac{k + 1}{2} \right)$
$\Rightarrow \frac{15}{2} = \frac{k^{2} - 1}{2} \Rightarrow k^{2} - 1 = 15 \Rightarrow k = \pm 4$